Time: 10:30-11:30 September 27, 2024 (Friday)
Venue: MCM410
Title: Geometric Langlands for Irregular Theta Connections and Epipelagic Representations
Abstract: Gradings on semisimple Lie algebras with stable vectors play an important role in representation theory. From stable vectors, Reeder and Yu constructed a family of supercuspidal representations called epipelagic representations. Over the function field of projective line, Yun globalized epipelagic representations using rigid automorphic data and constructed a family of Hecke eigensheaves. On the other hand, in the de Rham setting Yun also constructed an irregular connection on punctured projective line from a stable vector, called a theta connection. Chen proved that these connections are cohomologically rigid. In this talk, we will review these constructions and explain that theta connections and the Hecke eigensheaves of Yun match under geometric Langlands correspondence. This is a joint work with Tsao-Hsien Chen.
